@mister moose, since you appear to know more about physics than I, here's a question that I have. Is the equation f=mv^2/r the calculation only of centripetal force -- that is, the lateral force? If so, how does gravity interact with centripetal force to result in the perceived gravitational force, and what is the equation for that?
I'm not quite sure what you're asking. Also, once you go from single uniform objects to the real world it gets very complex. But in general, you need to be more specific. Remember the
m in the equation must be the mass that is being deflected or rotated. The
r must be the radius in the plane of rotary motion. So when you take these basic concepts and apply them to a real world situation, you need to keep that in mind. So what is lateral force? Are there components of another force acting in the same plane as the plane of rotation? Lateral to what? Is it changing? What is 'perceived gravitational force'? Whatever I choose to perceive?
Most of the questions I've been asking have been to get the group to think about other situations where their view still needs to apply. IE barstool vs ski turn. Does it still work there? If not, your view or description is likely flawed. Also, if we start with an assumption it will drive the conclusion. So if Bob Barnes is the definitive reference work of skiing, then his description of turning must be the correct and only one. I'm not commenting on the worth of Bob Barnes, only the process that got you there.
As far as forces interacting (Someone earlier used 'compose') they don't interact and become something different. Forces are additive. So in any case with multiple forces, simply add the forces together, but remember forces are vector quantities, and the math needs to reflect that. Who here took calculus? Remember Integration? That is the process of adding all the little bits together, letting the size of the bits move toward zero. It's an additive process.